How to solve this Diophantine Equation. Step by Step

Question

What are all the solutions to the diophantine equation: 6x-6y-xy=0.

Answer 1

Hint $\ $ Rewrite it as $\rm\: (6+x)(6-y) = 36.$

Answer 2

The 18 integer solutions are :

x = -42, y = 7

x = -24, y = 8

x = -18, y = 9

x = -15, y = 10

x = -12, y = 12

x = -10, y = 15

x = -9, y = 18

x = -8, y = 24

x = -7, y = 42

x = -5, y = -30

x = -4, y = -12

x = -3, y = -6

x = -2, y = -3

x = 0, y = 0

x = 3, y = 2

x = 6, y = 3

x = 12, y = 4

x = 30, y = 5